{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 逻辑回归解决多分类问题\n",
    "\n",
    "### 案例： 手写数字识别\n",
    "\n",
    "### 数据集：ex3data1.mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io as sio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = sio.loadmat('ex3data1.mat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'__header__': b'MATLAB 5.0 MAT-file, Platform: GLNXA64, Created on: Sun Oct 16 13:09:09 2011',\n",
       " '__version__': '1.0',\n",
       " '__globals__': [],\n",
       " 'X': array([[0., 0., 0., ..., 0., 0., 0.],\n",
       "        [0., 0., 0., ..., 0., 0., 0.],\n",
       "        [0., 0., 0., ..., 0., 0., 0.],\n",
       "        ...,\n",
       "        [0., 0., 0., ..., 0., 0., 0.],\n",
       "        [0., 0., 0., ..., 0., 0., 0.],\n",
       "        [0., 0., 0., ..., 0., 0., 0.]]),\n",
       " 'y': array([[10],\n",
       "        [10],\n",
       "        [10],\n",
       "        ...,\n",
       "        [ 9],\n",
       "        [ 9],\n",
       "        [ 9]], dtype=uint8)}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['__header__', '__version__', '__globals__', 'X', 'y'])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_X = data['X']\n",
    "raw_y = data['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5000, 400) (5000, 1)\n"
     ]
    }
   ],
   "source": [
    "print(raw_X.shape,raw_y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_an_image(X):\n",
    "    \n",
    "    pick_one = np.random.randint(5000)\n",
    "    \n",
    "    image = X[pick_one,:]\n",
    "    \n",
    "    fig,ax = plt.subplots(figsize=(1,1))\n",
    "    ax.imshow(image.reshape(20,20).T,cmap = 'gray_r')\n",
    "    \n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 72x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_an_image(raw_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_100_image(X):\n",
    "    \n",
    "    sample_index = np.random.choice(len(X),100)\n",
    "    images = X[sample_index,:]\n",
    "    print(images.shape)\n",
    "    \n",
    "    fig,ax = plt.subplots(ncols=10,nrows=10,figsize=(8,8),sharex=True,sharey=True)\n",
    "    \n",
    "    for r in range(10):\n",
    "        for c in range(10):\n",
    "            \n",
    "            ax[r,c].imshow(images[10 * r + c].reshape(20,20).T,cmap='gray_r')\n",
    "            \n",
    "    \n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    \n",
    "    plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 400)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_100_image(raw_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1/(1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costFunction(X,y,theta,lamda):\n",
    "    A = sigmoid(X@theta)\n",
    "    \n",
    "    first = y*np.log(A)\n",
    "    second = (1-y) * np.log(1-A)\n",
    "    \n",
    "    reg = np.sum(np.power(theta[1:],2)) * (lamda / (2 * len(X)))\n",
    "    \n",
    "    return -np.sum(first + second ) / len(X) + reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(X,y,theta,alpha,iters,lamda):\n",
    "    \n",
    "    costs = []\n",
    "    \n",
    "    for i in range(iters):\n",
    "        \n",
    "        reg = theta[1:] * (lamda / len(X))\n",
    "        reg = np.insert(reg,0,values=0,axis=0)\n",
    "        \n",
    "        theta = theta - (X.T@(sigmoid(X@theta) - y)) * alpha / len(X) -reg\n",
    "        cost = costFunction(X,y,theta,lamda)\n",
    "        costs.append(cost)\n",
    "        \n",
    "        if i % 1000 == 0:\n",
    "            print(cost)\n",
    "            \n",
    "    return theta,costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
